A Three-Parameter Lindley Distribution

Rama Shanker; Kamlesh Kumar Shukla; Ravi Shanker; Tekie Asehun Leonida

doi:10.5923/j.ajms.20170701.03

A Three-Parameter Lindley Distribution

Rama Shanker, Kamlesh Kumar Shukla, Ravi Shanker, Tekie Asehun Leonida

Stochastic Operations Research

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Abstract

A three-parameter Lindley distribution, which includes some two-parameter Lindley distributions introduced by Shanker and Mishra (2013 a, 2013 b), Shanker et al (2013), Shanker and Amanuel (2013), two-parameter gamma distribution, and one parameter exponential and Lindley distributions as special cases, has been proposed for modeling lifetime data. Its statistical properties including its shape, moments, skewness, kurtosis, hazard rate function, mean residual life function, stochastic ordering, mean deviations, order statistics, Renyi entropy measure, Bonferroni and Lorenz curves, stress-strength reliability have been discussed. For estimating its parameters, maximum likelihood estimation has been discussed. Finally, a numerical example has been presented to test the goodness of fit of the proposed distribution and the fit has been compared with the three-parameter generalized Lindley distribution.

Original language	English
Pages (from-to)	15-26
Journal	American Journal of Mathematics and Statistics
Volume	7
Issue number	1
DOIs	https://doi.org/10.5923/j.ajms.20170701.03
Publication status	Published - 2017

Keywords

Lindley distribution
Quasi Lindley distribution
Two-parameter Lindley distribution
Generalized Lindley distribution
Mathematical and Statistical properties
Moments
Maximum Likelihood estimation
Goodness of fit

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10.5923/j.ajms.20170701.03

2017-XShankerShuklaShankerLeonida_10.5923.j.ajms.20170701.03Final published version, 357 KB

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doi = "10.5923/j.ajms.20170701.03",

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A Three-Parameter Lindley Distribution

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Keywords

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